Question

The standard deviation of weekly net cash flows for the Pele Emergency Care Center is $1,000. Transactions costs sell securities to replenish cash is $25 each. The annualized interest rate earned on its marketable securities is 2.0%. Pele’s management likes to keep $2,000 as its minimum balance.

How much is the target cash balance C*?

How much is the average cash balance?

How much is the upper cash balance.

Answer 1

Solution:

Given data,

The standard deviation of weekly net cash flows for the Pele Emergency Care Center is $1,000.

Transactions costs sell securities to replenish cash is $25 each.

The annualized interest rate earned on its marketable securities is 2.0%.

Pele’s management likes to keep $2,000 as its minimum balance.

Answer :  How much is the target cash balance C?

Details	Amount($)
Transactions costs (TC)	$25
Variance of daily cash flow (V) = $1000/7	$142.86
Daily return on short term investments (r) = ((1+2%)^(1/365)) - 1	0.01%
Cash requirement minimum (L)	$2,000
Target cash balance (C) = [[(3*TC*V)/(4*r)]^1/3] + L	$2,366.85

Answer :  How much is the upper cash balance?

Upper cash balance (U) = 3C - 2L

= 3*$2,366.85 - 2*$2,000

= $3,100.55

Upper cash balance (U)

= $3,100.55

Answer :  How much is the average cash balance?

Average cash balance = (C + U)/3

= ($2,366.85 + $3,100.55)/3

= $1,822.47

Average cash balance

$1,822.47